Methods for determining risk and treating diseases and conditions that correlate to weather data

ABSTRACT

Methods and model equations are provided for predicting a risk of a subject who experiences adverse medical events associated with the weather, of experiencing a new-onset event. Methods include a) identifying a climate region of interest; b) collecting daily mean barometric pressure (BP) data for a time frame and dividing the days of the time frame into at least upper, middle and lower quantile BP days to identify the upper quantile BP days; c) collecting daily new onset event (NOE) data for a subject cohort consisting of subjects known to suffer from the adverse medical event for the time frame and calculating a daily incident rate (IR) of NOEs for each day of the time frame and dividing the days of the time frame into at least upper, middle and lower quantile IR-NOE days to identify the upper quantile IR-NOE (UQ-IR-NOE) days; d) determining a relevant number of seasons based on an association between the upper IR-NOE quantile days identified in c) and the upper BP quantile days identified in b); e) collecting hourly weather data for the time frame for a number of weather parameters and determining a set of weather variables; f) employing a generalized linear regression analysis to generate a rank for each weather variable as a predictor of the UQ-IR-NOE days for each relevant season, for each BP quantile; and g) identifying a risk-predictive equation using a forward stepwise approach to optimize fit and generate model equations useful for risk prediction. Development of a scalable model of risk-prediction for onset of new migraine headaches is detailed. Models for predicting hospital admissions and re-admissions and software products for implementation of the inventive methods and models by a computer are also provided.

PRIORITY CLAIM

This application claims priority under 35 U.S.C. § 119 to U.S.Provisional No. 62/046,681 filed Sep. 5, 2014, the entire disclosure ofwhich is incorporated herein.

TECHNICAL FIELD

The present invention relates generally to methods, products and modelsof risk management for experiencing adverse weather-associated symptomsof medical conditions and diseases.

BACKGROUND

Although as many as 80% of patients who suffer from migraine headachesimplicate “weather” as a trigger for migraine episodes, the evidencebased on clinical experience and epidemiologic studies is mixed. Not allpatients are equally as perceptive of weather parameters and not allpatients report the same weather factors as a trigger. Researchers haveattempted for years to more clearly delineate weather's role inpredicting migraine headache onset, typically evaluating individualmeteorological “weather” factors (e.g., barometric pressure,temperature, humidity, wind) as heterogeneous, continuous predictors ofmigraine. To date, none have developed a model with a high degree ofpredictive value, and some researchers have disparaged the concept dueto apparent inconsistency in the data.

For example, one study reported that low barometric pressure during thepreceding two days was associated with a higher frequency of emergencyroom visits for severe headache while others found the opposite or norelationship. Temperature has also shown mixed results; high temperaturein the preceding 24 hours has been found to increase emergency roomvisits for severe headache by 7.5% for every 5 degree increase intemperature, but other studies have found no effect of temperature onmigraine onset or severity.

Self-help internet sites (e.g., accuweather.com, weather.com) producedaily “migraine” risk models. However, the methodological development isnot apparently published or corroborated by any reports of predictiveaccuracy. These models tend to collapse migraine risk across regions ofthe country, which could be problematic as one cannot assume thetransportability of models from one location to another. The challengeof this and other models is that they can potentially do more harm thangood. When the predicted high-risk event fails to materialize (as isoften the case), patients become immune to future risk warnings and arethus unprepared when an actual event occurs. Alternatively, lumpinglarge areas of the country under a similar risk level makes theindividual less likely to personalize the information.

Another key problem with existing models is lack of scalability. Modelsgenerated from population data across varied climate regions, modelsgenerated from population data across a single climate region, andmodels generated from individual data in a single geographic area arenot equivalent predictors at the level of an individual.

A migraine early warning system would afford patients an invaluable toolto help them take steps to ward off and/or be prepared to combat apotential attack. Current models that tout a “migraine risk” predictorhave limited specificity and, as such, limited utility given their highfalse positive predictive rates.

Although migraine may be seen as the prototypical episodic disease eventgiven its propensity for being susceptible to changing weatherconditions, other diseases and health conditions also exhibit weatherdependency. For example, asthma, emphysema (COPD), depression, anxiety,osteoarthritis, fibromyalgia and stroke are all reported in theliterature as having a weather-based component to onset, flare-ups andseverity.

Conceptual and methodological barriers have impeded efforts to constructa reliable model for prediction of weather-based risk. First, mostresearchers and patients have considered weather parameters asindependent factors rather than evaluating them concurrently andconsecutively. Second, most have failed to consider how meteorologicalchanges may be especially predictive of weather-triggered health events.Third, many have only considered linear-based risk. Fourth, researchersoften fail to fully account for seasonal weather variations within andacross different climate regions. Finally, few have linked reoccurringweather patterns to migraine risk. Clearly, there remains a need in theart for valid, reliable models for predicting risk of weather-associateddiseases and medical conditions both for populations and at the level ofthe individual.

SUMMARY

Accordingly, the present investigators combined clinical, analytical,and technologic expertise from meteorology, headache medicine, andbioinformatics to develop predictive weather-based medical conditionrisk models, illustrated by detailed guidance in the development ofweather-based migraine headache risk-predictive models. Key innovationsinclude: 1) considering composite weather measures of both the absolute,central tendencies (mean, median), and differentials (i.e., changes inweather measures over varying time intervals); 2) evaluating theheterogeneity and interdependency of weather conditions via advancedstatistical modeling; 3) producing dynamic season specific models; and4) creating a customizable tiered migraine risk model.

The inventive methods are not limited to predicting migraine and may beapplied to generate predictive models for any weather-associated diseaseor condition, including, for example, hospital admission and readmissionrates. The methods and models are scalable to the level of an individualor to population studies, and are customizable across climate regionsand across seasons within climate regions, and are fully customizable toreflect unique weather-associated triggers of a given patient. Thefeatures of accounting for the interdependency of weather measurements,evaluating varying weather observations and change at varying intervals,allowing for non-linear seasonal variations, acquiring average weatherconditions over a defined geographic area, and creating customizabletiered risk models, when combined, can be applied to a host of diseaseentities.

One embodiment of the invention provides methods for generating modelsets of equations for predicting a risk of a subject who experiencesadverse medical events associated with the weather, of experiencing anew-onset event (NOE). The methods comprise: a) identifying a climateregion of interest; b) collecting daily mean barometric pressure (BP)data for a time frame and dividing the days of the time frame into atleast upper, middle and lower quantile BP days to identify the upperquantile BP days; c) collecting daily NOE data for a subject cohortconsisting of subjects known to suffer from the adverse medical eventfor the time frame and calculating a daily incident rate (IR) of NOEsfor each day of the time frame and dividing the days of the time frameinto at least upper, middle and lower quantile IR-NOE days to identifythe upper quantile IR-NOE (UQ-IR-NOE) days; d) determining a relevantnumber of seasons based on an association between the upper IR-NOEquantile days identified in c) and the upper BP quantile days identifiedin b); e) collecting hourly weather data for the time frame for a numberof weather parameters and determining a set of weather variables; f)employing a generalized linear regression analysis to generate a rankfor each weather variable as a predictor of the UQ-IR-NOE days for eachrelevant season, for each BP quantile; g) identifying a risk-predictiveequation using a forward stepwise approach.

The generated model comprises a set of one or more equations forpredicting the risk of a subject experiencing a new-onset event (NOE) atthe completion of step g. Different climate regions and differentmedical conditions may involve a different number of relevant seasons.In specific embodiments, regression analysis of the UQ-BP days and theUQ-IR-NOE days across a time frame (for example, one year) may be usedto determine a number of relevant seasons. For example, for patientssuffering from migraine headaches, which are known to beweather-associated, and residing in the Köppen-Geiger climate regionCfa, the regression analysis revealed two relevant seasons, referred toin very specific embodiments disclosed herein as F/W/S and Summer.

According to some embodiments, model equations may be used to predict arisk of a patient suffering from a new onset event on a future day. Inspecific embodiments, a risk-predictive model set of equations isgenerated for patients suffering from migraine headaches and residing inclimate region Cfa:

1. [season=F/W/S, BP tertile=lower]

R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(B]) +N+ε or 1=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ²^(A(exp)2+β) ³ ^(B+β) ⁴ ^(B(exp)2]) +N+ε

2. [season=F/W/S, BP tertile=middle]

R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(B]) +N+ε

3. [season=F/W/S, BP tertile=upper]

R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(C]) +N+ε

4. [season=Summer, BP tertile=lower]

R=e ^([β) ⁰ ^(+β) ¹ ^(E]) +N+ε

5. [season=Summer, BP tertile=middle]

R=e ^([β) ⁰ ^(+β) ¹ ^(G+β) ² ^(F]) +N+ε

6. [season=Summer, BP tertile=upper]

R=e ^([β) ⁰ ^(+β) ¹ ^(H]) +N+ε

wherein R is the risk, N is the number of subjects in the cohorteligible to have a new onset headache (NOH) on a given day and is thedenominator in the IR-NOH calculation, and c is an error term of GEEregression modeling.

Other weather-implicated diseases and/or medical conditions susceptibleto risk-predictive modeling according to embodiments of the inventioninclude, but are not limited to, asthma, emphysema, depression,cardiovascular disease, arthritis, atherosclerosis, and diabetes.

According to specific embodiments, once a risk-predictive model isgenerated according to the invention, the subject may predict a risk ofexperiencing a new onset event on a future day by identifying anappropriate model equation based on the subject's residential climateregion, the season, and the predicted BP on the future day, and thenentering the predicted weather data called for by the appropriateequation.

A further embodiment provides methods for increasing efficiency in ahospital staffing and resource commitment by predicting high admissiondays, a “high” admission day being defined as a day falling in an upperquantile of the hospital's daily admissions for a year. The methodscomprise: 1) generating a model set of equations for predicting a riskof subjects who suffer from weather-implicated medical conditions ofbeing admitted to the hospital, wherein “generating” comprises the stepsof: a) identifying the climate region in which the hospital is located;b) collecting daily mean barometric pressure (BP) data for the year anddividing the mean BP data into upper, lower and middle quantiles; c)collecting daily hospital admissions data for a subject cohort for theyear, said subject cohort consisting of subjects known to suffer from aweather-implicated medical condition and who have been admitted to ahospital at least once previously due to experiencing an adverse eventassociated with the condition, to calculate a daily admission rate (AR)for each day of the year and to determine an upper quantile of daysassociated with the AR; d) determining a number of relevant seasonsbased on regression analysis of the upper BP quantile days and the upperAR quantile days; e) collecting weather parameter data across the year;f) employing GEE modeling to generate a rank for each weather variableas a continuous predictor of the upper quantile AR days for eachrelevant season, for each BP quantile; g) identifying a best predictivesingle variable equation based on p-value and QIC fit of thefirst-ranked weather variable in each relevant season, for each BPquantile; h) adding the next-ranked weather variable to the identifiedequation from g) in each season, for each BP and determining if fitimproves; and i) repeating step h) until addition of the next-rankedweather variable fails to improve fit, wherein the model comprises a setof equations for predicting a risk of subjects who suffer fromweather-implicated medical conditions of being admitted to the hospitalat the completion of step i); 2) employing the model to determine whichdays are likely to be upper quantile admission rate (UQ-AR) days; and 3)staffing the hospital and committing resources to the hospital on thebasis of the determination in step 2).

Embodiments are also directed to articles of manufacture comprisingcomputer-readable code for implementing methods for predicting risk ofexperiencing a new onset symptom such as a migraine headache inaccordance with embodiments of the invention. In specific embodimentsthe article comprises a mobile application software product.

These and other embodiments and aspects of the invention we be furtherclarified and understood by reference to the Figures and DetailedDescription herein.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1. Depicts a schematic flow chart of general data input steps inthe model for predicting risk of a new onset headache.

FIG. 2. An empirically generated flow-chart showing percentage of upperBP tertile days during the F/W/S season in which a New Onset Headache(NOH) was experienced as a function of particular weather variables.

FIG. 3. An empirically generated flow-chart showing percentage of middleBP tertile days during the F/W/S season in which an NOH occurred as afunction of particular weather variables.

FIG. 4. An empirically generated flow-chart showing percentage of lowerBP tertile days during the F/W/S season in which an NOH occurred as afunction of particular weather variables.

FIG. 5. 5A) Generalized Additive Model (GAM) based on the original dataset for lower BP tertile in the F/W/S season; 5B) Generalized EstimatingEquation model based on the same original data set; 5C) two bestBootstrap Models for re-sampled data.

FIG. 6. 6A) Generalized Additive Model (GAM) based on the original dataset for middle BP tertile in the F/W/S season; 6B) GeneralizedEstimating Equation model based on the same original data set; 6C) bestBootstrap Model for re-sampled data.

FIG. 7. 7A) Generalized Additive Model (GAM) based on the original dataset for upper BP tertile in the F/W/S season; 7B) Generalized EstimatingEquation model based on the same original data set; 7C) three bestBootstrap Models for re-sampled data.

FIG. 8. 8A) Generalized Additive Model (GAM) based on the original dataset for lower BP tertile in the Summer season; 8B) GeneralizedEstimating Equation model based on the same original data set; 8C) twobest Bootstrap Models for re-sampled data.

FIG. 9. 9A) Generalized Additive Model (GAM) based on the original dataset for middle BP tertile in the Summer season; 9B) GeneralizedEstimating Equation model based on the same original data set; 9C) twobest Bootstrap Models for re-sampled data.

FIG. 10. 10A) Generalized Additive Model (GAM) based on the originaldata set for upper BP tertile in the Summer season; 10B) GeneralizedEstimating Equation model based on the same original data set; 10C) twobest Bootstrap Models for re-sampled data.

FIG. 11. A Köppen climate classification map and key for North America

DETAILED DESCRIPTION

Highly reliable weather based models for predicting risk of experiencinga new-onset symptom of a weather-associated disease or condition aredetailed herein. The inventive models are characterized by their dynamicnature and scalability by leveraging the heterogeneity of weatherfactors.

Models generated in accordance with aspects of the invention arecontemplated as climate region-specific, although derivation of a modelis similar regardless of climate and there may be between-climate regionoverlap. Any climate classification scheme is suitable so long asmodel-generation data is derived from the same classified climate regionas the residence of a subject or from the climate region of the areaunder risk assessment. According to specific embodiments of theinvention the risk-predictive models are generated for climate regionsclassified under the Köppen climate classification scheme, which dividesclimates into five main groups (A, B, C, D, E), each having severaltypes and subtypes. Each particular climate type is represented by atwo- to four-letter symbol. The Köppen climate classification is basedon the empirical relationship between climate and vegetation andprovides an efficient way to describe climatic conditions defined bytemperature and precipitation and their seasonality with a singlemetric. The present investigators discovered that the seasonal variation(or lack thereof) within a climate region impacts a predictive model forresidents of the climate region. The five main Köppen groups include:

GROUP A: Tropical/megathermal climates—characterized by constant hightemperatures (at sea level and low elevations) across the year andincludes tropical rainforest (Af) tropical monsoon (Am) and tropicalsavanna (Aw, As).GROUP B: Dry (arid and semiarid) climates; characterized by actualprecipitation less than a threshold value set equal to the potentialevapotranspiration, and includes desert (BWh, BWk), and semi-arid (BSh,BSk).GROUP C: Temperate/mesothermal climates; characterized by an averagemonthly temperature above 10° C. (50° F.) in their warmest months, andan average monthly temperature above −3° C. (27° F.) in their coldestmonths, and includes humid subtropical (Cfa, Cwa), oceanic (Cfb, Cwb,Cfc, Cwc), and Mediterranean (Csa, Csb).GROUP D: Continental/microthermal climates; characterized by an averagetemperature above 10° C. (50° F.) in their warmest months, and a coldestmonth average below −3° C. (or 0° C. in some versions, as notedpreviously), and includes humid continental (Dfa, Dwa, Dfb, Dwb, Dsa,Dsb), and subarctic (Dfc, Dwc, Dfd, Dwd, Dsc, Dsd).GROUP E: Polar and Alpine climates; characterized by averagetemperatures below 10° C. in all 12 months of the year, and includestundra (ET), ice cap (EF), and alpine (ET, EF).GROUP H: climates that are strongly influenced by the effects ofaltitude. As a result, the climate of such locations is different fromplaces with low elevations at similar latitudes.

The Köppen classification scheme applied to North America is set forthas FIG. 11, with attribution to A Peel, M. C. and Finlayson, B. L. andMcMahon, T. A. (2007). “Updated world map of the Köppen-Geiger climateclassification.” Hydrol. Earth Syst. Sci. 11: 1633-1644.doi:10.5194/hess-11-1633-2007, the entire disclosure of which isincorporated herein by this reference.

Particular embodiments of the invention provide methods for generatingmodel sets of equations for predicting a risk of a subject whoexperiences adverse medical events associated with the weather, ofexperiencing a new-onset event (NOE). The methods comprise: a)identifying a climate region of interest; b) collecting daily meanbarometric pressure (BP) data for a time frame and dividing the days ofthe time frame into at least upper, middle and lower quantile BP days toidentify the upper quantile BP days; c) collecting daily NOE data for asubject cohort consisting of subjects known to suffer from the adversemedical event for the time frame and calculating a daily incident rate(IR) of NOEs for each day of the time frame and dividing the days of thetime frame into at least upper, middle and lower quantile IR-NOE days toidentify the upper quantile IR-NOE (UQ-IR-NOE) days; d) determining arelevant number of seasons based on an association between the upperIR-NOE quantile days identified in c) and the upper BP quantile daysidentified in b); e) collecting hourly weather data for the time framefor a number of weather parameters and determining a set of weathervariables; f) employing a generalized linear regression analysis togenerate a rank for each weather variable as a predictor of theUQ-IR-NOE days for each relevant season, for each BP quantile; g)identifying a risk-predictive equation using a forward stepwiseapproach. According to specific embodiments, the number of relevantseasons is 1, 2, 3 or 4 and the time frame is a time frame encompassingat least a portion of each relevant season. In more specific embodimentsthe time frame is for one year. The term “year” herein may include anumber of days approximating one year. In specific embodiments one yearis between 300 and 400 days, between 320 and 380 days, between 340 and370 days, or 365 days±5 days.

According to specific embodiments, the generalized linear regressionanalysis comprises a generalized linear mixed model (GLMM) analysis (seeJiang, J. (2007), Linear and Generalized Linear Mixed Models and TheirApplications, Springer, the entire disclosure of which is incorporatedherein by this reference). According to other embodiments thegeneralized linear regression analysis comprises a generalizedestimating equation (GEE) analysis (see, e.g. Hardin, James; Hilbe,Joseph (2003). Generalized Estimating Equations. London: Chapman andHall/CRC, the entire disclosure of which is incorporated herein by thisreference. Software for solving generalized estimating equations isavailable in MATLAB, SAS (proc genmod), SPSS (the gee procedure), Stata(the xtgee command) and R (packages gee, geepack and multgee). Incertain aspects a generalized linear regression analysis is used togenerate a rank for each weather variable as a continuous predictor ofthe UQ-IR-NOE days for each relevant season.

In specific embodiments, the generalized linear regression analysis stepcomprises GEE and the forward stepwise approach of step (g) comprisesthe following steps: i) identifying a best predictive single variableequation based on p-value and quasi-likelihood independence criterion(QIC) fit of the first-ranked weather variable in each season, for eachBP quantile; ii) adding the next-ranked weather variable to theidentified equation from g) in each season, for each BP and determine iffit improves; and iii) repeating step (ii) until addition of thenext-ranked weather variable to the model fails to improve fit. In otherspecific embodiments the generalized linear regression analysiscomprises a generalized mixed regression analysis and the forwardstepwise approach of step (g) comprises the following steps: i)identifying a best predictive single variable equation based on Akaikeinformation criterion (AIC) fit of the first-ranked variable in eachseason, for each BP quantile; ii) adding the next-ranked weathervariable to the identified equation from (g) in each season, for each BPand determine if fit improves; and iii) repeating step (ii) untiladdition of the next-ranked variable to the model fails to improve fit.

The number of relevant seasons may be determined based on a regressionanalysis of the UQ-BP and the UQ-IR-NOE. The regression analysiscomprises one or both of leverage point diagnostics and outlierdetection diagnostics. After fitting a regression model, diagnostics areused to determine whether all the necessary model assumptions are valid.Relevant seasons are defined as periods of the year in which differentmodel equations are valid.

Daily incident rate is equal to the number of subjects experiencing anNOE divided by the total number of eligible subjects. In specificembodiments, an “eligible subject” is defined as a subject who has notexperienced an event in the preceding 24 hours. An “event” in thiscontext is measured from the onset of a symptom until the subjectreturns to a normal, pre-symptom state. For example, where an event isexperiencing a migraine headache, an eligible subject has notexperienced a headache in the last 24 hours, regardless of the time ofonset of the last-experienced headache. In another specific example,where an event is experiencing an outbreak of psoriasis, an eligiblesubject has been completely clear of psoriasis for the last 24 hours.According to yet another specific example, where an event isexperiencing arthritic joint pain, an eligible subject did notexperience joint pain in the last 24 hours.

In specific embodiments, the subject cohort is further controlledaccording to factors known to influence frequency of a medical conditionunderpinning an adverse event associated with the weather. For example,the cohort may be controlled for race, gender, age, socio-economicstatus, co-morbidities, tobacco use, alcohol use and general health ofthe subject, which may further increase the predictive reliability ofthe model for some subjects.

Weather variables in accordance with aspects of the invention are basedon weather parameters including but not limited to barometric pressure(BP), wind speed (WS), wind direction (WD), dry bulb temperature (DBT),lightening activity (LA), relative humidity (RH), and precipitation (P).Weather variables may comprise daily mean and multiple differentialmaximums, minimums and means for each selected parameter. Multipledifferentials are selected from a 24 hour differential, a 12 hourdifferential, a 6 hour differential a 3 hour differential, andcombinations thereof for each selected parameter. Weather parameter dataaccording to specific aspects may be gathered by looking up data forhistorical time periods or by looking up forecast data for future timeframes. Databases include, for example, Climate Data Online atwww.ncdc.noaa.gov/cdo-web/, and the National Weather Service Forecastdata www.weather.gov/forecastmap.

As noted above, the Köppen climate classification system divides theearth into six main climate regions designated by capital letters A, B,C, D, E and H, and over 20 sub-regions. Risk-predictive models accordingto embodiments of the invention are climate-region specific. Preferably,in generating a model, data is collected from multiple locations acrossa selected region or sub-region, and integrated. Example 1 illustratesdata collection from five locations in Köppen climate sub-region Cfa.The regression analysis of the UQ-NOE and UQ-BP data collected in thisregion revealed two relevant seasons (validity of a model as assessed bymodel diagnostics exists within a relevant season). The relevant seasonsfor climate region Cfa are referred to herein as F/W/S corresponding tothe time frame of from the fall equinox to the summer solstice, e.g.9/21-6/20, and Summer, corresponding to the time frame of the summersolstice to the Fall equinox, e.g. 6/21-9/20).

According to very specific embodiments, the weather associated adverseevent is experiencing a new onset of a migraine headache (NOE=NOH), thequantile is a tertile and the model set of equations includes thefollowing determined weather variables: A) BP 24 hour differential mean;B) WS 24 hour differential maximum; C) DBT 24 hour differential mean; D)DBT 6 hour differential mean; E) BP 24 hour differential maximum; F) DBTdaily mean; G) BP daily mean; and H) RH 24 hour differential mean. Otherapplicable quantiles include quartiles, quintiles, sextiles, deciles,and percentiles. The upper, middle and lower quantiles having moreranking divisions than tertiles are defined as any grouping thatcontains the uppermost quantile, any grouping that contains themiddle-most quantile, and any grouping that contains the lower-mostquantile, respectively.

A specific and non-limiting example of a risk predictive model set ofequations generated according to the guidance provided in the Examplesand specific to the Cfa climate region, where R=risk of a given daybeing a UT-IR-NOH day, comprises:

1. [season=F/W/S, BP tertile=lower]

R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(B]) +N+ε or 1=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ²^(A(exp)2+β) ³ ^(B+β) ⁴ ^(B(exp)2]) +N+ε

2. [season=F/W/S, BP tertile=middle]

R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(B]) +N+ε

3. [season=F/W/S, BP tertile=upper]

R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(C]) +N+ε

4. [season=Summer, BP tertile=lower]

R=e ^([β) ⁰ ^(+β) ¹ ^(E]) +N+ε

5. [season=Summer, BP tertile=middle]

R=e ^([β) ⁰ ^(+β) ¹ ^(G+β) ² ^(F]) +N+ε

6. [season=Summer, BP tertile=upper]

R=e ^([β) ⁰ ^(+β) ¹ ^(H]) +N+ε

wherein N is the number of subjects in the cohort eligible to have anNOH on a given day and is the denominator in the IR-NOH calculation, andε is an error term of GEE regression modeling. Weather variables aresymbolized by the capital letter designations of the preceding paragraphfor clarity.

Particular embodiments of methods of the invention are applicable at thelevel of an individual. A risk-predictive model is generated for aclimate region, then subjects who experience weather-associated adverseevents and who are residents of or visitors to the climate region mayutilize the model to assess personal risk of experiencing a new onsetadverse event on a given day, either present or future. According to oneembodiment, the method comprises a) determining a climate regionassociated with the geographical location of the subject on the givenday; b) determining the relevant season in which the given day falls; c)determining the projected mean BP for the day and identifying the givenday as an upper, middle or lower quantile BP day; d) selecting anequation from a risk-predictive model set of equations generated for thedetermined climate region, determined relevant season and determined BPquantile; and e) entering weather variable data forecast for the givenday into the selected equation to yield an assessment of the risk. Thesubject may then undertake treatment to avoid or mitigate the adverseevent. In specific embodiments, the weather-implicated adverse event isassociated with a condition selected from migraine headache, asthma,emphysema, depression, cardiovascular disease, arthritis,atherosclerosis, psoriasis and diabetes. In very specific embodiments,the adverse event is associated with atherosclerosis and comprises heartattack or stroke. In other very specific embodiments the adverse eventis associated with arthritis and is joint pain. In other very specificembodiments the adverse event is associated with migraine headaches andcomprises experiencing a new onset migraine headache.

In accordance with specific method embodiments where the adverse eventis experiencing a new onset migraine headache and the subject resides inclimate region Cfa, the method comprises: a) determining the relevantseason in which the given day falls; b) determining whether the givenday is an upper, middle or lower BP tertile day; c) selecting anequation from the model set of equations according to claim 16 specificto the determined relevant season and the determined BP tertile; d)entering weather variable data for the given day into the selectedequation to yield an assessment of the risk.

Ultimately, when scaled to the individual subject, embodiments of therisk-predictive models are intended to provide enhanced symptommanagement and mitigating/preventative treatment benefits to a subjectwho suffers from a weather-associated medical condition or disease. Forexample, if a subject known to suffer from weather-associated migraineheadaches utilizes an inventive model to determine that agreater-than-not risk exists tomorrow for experiencing a new onsetmigraine headache, the subject may undertake preventative or mitigatingtreatment at a point where such treatment is most effective—prior toonset of clinical symptoms. It is contemplated therefore thatembodiments of the inventive models may be incorporated into individualtreatment regimens by clinicians.

Non-limiting examples of migraine headache preventative interventionsand treatments which may be undertaken upon determination of agreater-than-not risk include: cardiovascular drugs such as the betablockers exemplified by triptans exemplified by frovatriptan (Frova),sumatriptan (Imitrex), rizatriptan (Maxalt), zolmitriptan (Zomig),almotriptan (Axert), electriptan (Relpax), naratriptan (Amerge);propranolol (Inderal La, Innopran XL, others), metoprolol tartrate(Lopressor) and timolol (Betimol); calcium channel blockers exemplifiedby Verapamil (Calan, Verelan, others); angiotensin-converting enzymeinhibitors exemplified by lisinopril (Zestril); antidepressants such asthe tricyclic antidepressants exemplified by Amitriptyline, andserotonin and norepinephrine reuptake inhibitors exemplified byvenlafaxine (Effexor XR); anti-seizure drugs exemplified by valproatesodium (Depacon) and topiramate (Topamax); and pain relievers such asnonsteroidal anti-inflammatory drugs exemplified by naproxen (Naprosyn).

According to some embodiments, weather predictive risk models may beutilized to predict hospital admissions/readmissions. The models mayidentify high risk days for hospital admissions for commonweather-associated disorders including, for example, asthma, emphysema,depression, heart attack, and stroke. Preventative medical treatmentsmay be optimized on high risk days to decrease admission and rate ofreadmission to hospitals/clinics. Staffing and resource commitment maybe allocated according to high versus low risk days based on the model.

Readmission is a major problem for U.S. health care efficiency. Eighteenpercent of all Medicare patients are readmitted to the hospital withinone month of release. In the context of Medicare, admissions carry steeppenalties and the cost to the US economy is estimated to be 26 billiondollars, of which approximately 17 billion is preventable. Currently,care management programs constitute a thriving medical side industryaimed at reducing these numbers.

One embodiment is directed to methods for increasing efficiency inhospital staffing and resource commitment by predicting high admissiondays, a “high” admission day being defined as a day falling in an upperquantile of the hospital's daily admissions for a year. According to onespecific embodiment the method comprises: generating a model set ofequations for predicting a risk of subjects who suffer fromweather-associated medical conditions of being admitted to the hospital,wherein “generating” comprises the steps of: identifying the climateregion in which the hospital is located; collecting daily meanbarometric pressure (BP) data for the year and dividing the mean BP datainto upper, lower and middle quantiles; collecting daily hospitaladmissions data for a subject cohort for the year, said subject cohortconsisting of subjects known to suffer from a weather-associated medicalcondition and who have been admitted to a hospital at least oncepreviously due to experiencing an adverse event associated with thecondition, to calculate a daily admission rate (AR) for each day of theyear and to determine an upper quantile of days associated with the AR;determining a number of relevant seasons based on regression analysis ofthe upper BP quantile days and the upper AR quantile days; collectingweather parameter data across the year; employing GEE modeling togenerate a rank for each weather variable as a continuous predictor ofthe upper quantile AR days for each relevant season, for each BPquantile; identifying a best predictive single variable equation basedon p-value and QIC fit of the first-ranked weather variable in eachrelevant season, for each BP quantile; adding the next-ranked weathervariable to the identified equation from g) in each season, for each BPand determining if fit improves; repeating step h) until addition of thenext-ranked weather variable fails to improve fit, wherein the modelcomprises a set of equations for predicting a risk of subjects whosuffer from weather-associated medical conditions of being admitted tothe hospital at the completion of step i); employing the model todetermine which days are likely to be upper quantile admission rate(UQ-AR) days; and staffing the hospital and committing resources to thehospital on the basis of the determination in step 2).

According to another specific embodiment, an article of manufacturecomprising computer readable code for implementing methods according tothe invention is provided. A very specific embodiment comprises mobileapplication weather-based risk prediction software for implementing themethods of the invention by a mobile device such as a smart phone,tablet, smart watch and the like, enabling real-time risk prediction tosubjects who suffer from weather-implicated conditions. Response to therisk may be proactive and designed to manage the risk. For example,medications and treatments are available that are effective inmitigating the severity or preventing onset of symptoms of manyweather-implicated diseases and conditions, including migraineheadaches. The software may be customizable by a patient according togeographical area of residence and patient-specific historical data. Forexample, in creating a risk predictive model, the patient's medicalhistory may be utilized to generate a model set of equations across anytime frame desired. In other specific embodiments the software respondsto user input by adapting the risk-predictive model to actual outcomes.

According to specific embodiments, including personalized mobileapplication embodiments, an initial query is to identify whether thedisease or condition of a given patient is weather-associated withrespect to the individual patient. For example, the patient may berequested to keep a symptom log for a period of time ranging from about30 to about 60, 90, 120 or 180 days. The patient's individual incidencerate is correlated to the weather data across the same period of timefor weather variables found to be significant at a population level forthe particular disease or condition, and the set of weathervariables/differentials significant to predicting risk in the individualpatient is determined. With enough data specific cut-points for theweather variables may also be determined at the level of the individualand model equations predictive at the level of an individual patient maybe ascertained. Embodiments are contemplated whereby the programmedmodel equations may be utilized by the patient to predict risk ofexperiencing a symptom associated with the disease or condition on afuture day utilizing weather data forecast databases to calculateestimated risk. Degree of risk may also be a programmable output. Suchdatabases are provided, for example, by the U.S. National WeatherService at www.weather.gov/forecastmap. Based on the individualpatient's needs, prophylactic treatment may be undertaken or a schedulemay be adjusted in response to the calculated risk.

EXAMPLES

The following examples are set forth to illustrate particular aspectsand features of the invention and should not be construed as limitingthe full scope of the invention as defined by the claims.

Example 1

The following example illustrates derivation of a risk-predictive modelset of equations applicable to residents of climate region Cfa.Therefore, the stated seasons correspond to the following dates:Summer—6/21 to 9/20; Fall—9/21 to 12/20; Winter—12/21 to 3/20;Spring—3/21 to 6/20. As detailed below, it was determined that for theCfa climate region, there are two model-relevant seasons: F/W/Scorresponding to the dates of 9/21 to 6/20; and Summer corresponding tothe dates of 6/21 to 9/20.

Illustrative inventive risk-predictive models were developed fromheadache data obtained from subjects suffering from migraine headachesresiding in St. Louis, Mo. Each subject completed a daily headache diaryfor 2-6 months recording the presence or absence of headache. Therefore,multiple persons recorded headache data on the same days.

The primary outcome measure for the study was whether a specific day'sincidence rate (IR) of new onset headache (NOH) was among the top thirdof daily IR-NOH during the season in which that day fell. Those daysthat did have daily IR-NOH rates among the top third for that seasonwere considered to be in the upper tertile (UT) for that season (andwere labeled “UT-IR-NOH”). NOH was defined as the presence of headacheon a given day coupled with the absence of headache on the preceding dayfor an individual. Daily NOH incidence (IR-NOH) were then calculated.The daily IR-NOH numerator was the total number of individuals with NOHon a given day and the denominator was the total number of individualseligible to have NOH on that same day. Subjects were excluded from thedenominator if they had a headache the day before because by definitionthey could not have had a “new” headache that day. For example, if 25subjects recorded on a given day, but five of them had a headache theday before then the daily IR-NOH only included data from 20participants. Daily IR-NOH for each season was then calculated and thehighest 33% of daily IR-NOH rates for that season were designated asbeing UT-IR-NOH.

A full suite of hourly weather data was obtained from the NationalWeather Service for five different weather stations located in the St.Louis area for each day of the study. The weather variables measuredhourly included barometric pressure (BP), relative humidity (RH), drybulb temperature (DBT), wind direction (WD), and wind speed (WS). Themaximum, minimum, and mean values of these variables were recorded. Thehourly weather measurements from the five weather stations were averagedto come up with average representative weather variables for a given dayin the St. Louis metro area. 3, 6, 12, 24 and 48 hour weatherdifferentials were also calculated based on these representative weathervariables. A weather differential was defined as the value of theweather variable at time 0 minus that from a preceding time period(weather variable_(Time0)−weather variable_(PrecedingTime)=weatherdifferential).

The relative risks of a day being a UT-IR-NOH for that season werecalculated using a Poisson regression model with a robust errorvariance. This methodology has been shown to be reliable in simulatedand real data sets of various sizes and outcome incidence rates. Theindependent variables for these statistical models included the dailymaximums, minimums and means of the weather variables at time 0 andother time intervals. The natural log of the number of subjectsreporting their headache status on a given day was defined as the offsetvariable. The GEE model used an independent correlation structure, asubject effect of “day” representing each unique day in the analysis,and a within-subject effect of “ID” representing a unique identificationnumber for every subject in the cohort.

Initial analysis suggested that BP was particularly important indetermining which days were UT-IR-NOH. Moreover, it appeared that thedays with the highest and lowest BP modeled different types of weather.Thus, prior to modeling daily UT-IR-NOH risk, daily mean BP distributionacross each season was split into season specific categories; uppertertile, middle tertile, lower tertile. In addition, fall, winter andspring modeled similarly and were thus combined into one analysis. Thesummer season modeled differently from the other seasons and was modeledseparately. A stratified analysis was performed on each seasonal groupbased upon mean BP tertiles. Therefore, there were a total of sixstratified models (e.g. models of fall/winter/spring and summer for eachof the three BP tertiles). In addition, alternative models offall/winter/spring and all four seasons together that combined the lowand middle tertiles of mean BP were also run.

In an effort to develop the optimal seasonal models, GEEs were employedto model each of the different weather variables as continuouspredictors of UT-IR-NOH days. The p-values and quasi-likelihood underthe independence model criterion (QIC) fit statistics for these modelswere obtained and the “best” single variable models were selected. Theanalysis was then repeated with the second most predictive weathervariable being added to the model. If the second variable improved thefit of the model, then the “best” two variable models were selected andincorporated in a generalized additive model to identify potentialcut-points for each variable. These variables were then entered in asecond GEE model to determine the optimal models based upon QIC fitstatistics. Some models included weather variables with specific cutpoints while others modeled the weather variable continuously.

Examples 2-7 set forth actual models that were found to be predictivefor each of the stratified analyses. The weather variables used in themodels are defined below:

-   -   1) BP 24 hour differential mean (BP_24hr_Diff_Mean) was        calculated by subtracting the hourly BP from the preceding day        (day−1) from that from the following day (Hourly        BP_(Day 0)−Hourly BP_(Day−1) at exactly the same time of each        day. For example, the 1:00 AM BP from day−1 would be subtracted        from the 1:00 AM BP on day 0. Therefore we obtained 24        differentials for a given day. The mean of these 24 hourly        differentials was the BP_24hr_Diff_Mean for day 0.    -   2) WS 24 hour differential maximum (WS_24hr_Diff_Max) was        calculated by subtracting the hourly WS from the preceding day        (day−1) from that from the following day (Hourly        WS_(Day 0)−Hourly WS_(Day−1)) at the same time. Therefore we        obtained 24 differentials for a given day. The maximum of these        24 hourly differentials was the WS_24hr_Diff_Max for day 0.    -   3) DBT 24 hour differential mean (DBT 24hr_Diff_Mean) was        calculated by subtracting the hourly DBTs from the preceding day        (day−1) from that from the following day (Hourly        DBT_(Day 0)−Hourly DBT_(Day−1)). Therefore we obtained 24        differentials for a given day. The mean of these 24 hourly        differentials was the DBT_24hr_Diff_Mean for day 0.    -   4) DBT 6 hour differential mean (DBT_6 hr_Diff_Mean) was        calculated by subtracting the hourly DBT from 6 hours prior from        that from that at a given hour during a day (Hourly        DBT_(Any hour during the day)−Hourly DBT_(6 hours prior)). For        example, the hourly DBT from 3:00 AM was subtracted from the        hourly DBT from 9:00 AM. Therefore, we obtained 24 six hour        differentials for a given day. The mean of these 24 hourly        differentials was the DBT_6 hr_Diff_Mean for day 0.    -   5) BP_24 hour differential maximum (BP_24hr_Diff_Max) was        calculated by subtracting the hourly BP from the preceding day        (day−1) from that from the following day (Hourly        BP_(Day 0)−Hourly BP_(Day−1)). Therefore we obtained 24        differentials for a given day. The maximum of these 24 hourly        differentials was the BP_24hr_Diff_Max for day 0.    -   6) DBT daily mean (DBT_Daily_Mean) was defined as the mean of        the 24 hourly measurements of DBT.    -   7) BP daily mean (BP_Daily_Mean) was defined as the mean of the        24 hourly measurements of BP.    -   8) RH 24 hour differential mean (RH_24hr_Diff_Mean) was        calculated by subtracting the hourly humidity from the preceding        day (day−1) from that from the following day (Hourly        RH_(Day 0)−Hourly RH_(Day−1)). Therefore we obtained 24        differentials for a given day. The mean of these 24 hourly        differentials was the RH_24hr_Diff_Mean for day 0.

Example 2

This example illustrates generation of four model equations for lowertertile BP days in the F/W/S season,

For the first, second and third model equations:Outcome variable: UT-IR-NOH

1=Yes; the day is a UT-IR-NOH day for the season

0=No; the day is not a UT-IR-NOH day for the season

The intercept is represented by β₀

First predictor variable: BP_Diff_Mean_Low

1=Yes; the day had a BP_24hr_Diff_Mean ≤0.0

0=No; the day did not have a BP_24hr_Diff_Mean ≤0.0

The coefficient for the predictor variable BP_Diff_Mean_Low isrepresented by β₁

Second predictor variable: WS_Diff_Max_ge_7

1=Yes; the day had a WS_24hr_Diff_Max ≥7

0=No; the day did NOT have a WS_24hr_Diff_Max ≥7

The coefficient for the predictor variable WS_Diff_Max_ge_7 isrepresented by β₂

Offset term—variable log(N), where N=the number of patients eligible tohave a NOH on the given day.Error term of GEE regression model represented by “ε”.First Model Equation for lower BP tertile, F/W/S season: (estimated){circumflex over (β)}₀=−6.2589; {circumflex over (β)}₁=6.2589 and{circumflex over (β)}₂=0.9731.

Model Information Data Set WORK.FWS_LOW_BP_1 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (200 levels) Subject Effect Date (90 levels) Number ofClusters 90 Correlation Matrix 200 Dimension Maximum Cluster Size 99Minimum Cluster Size 28

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.2589 0.4589 −7.1583 −5.3596 −13.64 <.0001 BP_Diff_Mean_Low1 1.1736 0.4575 0.2770 2.0702 2.57 0.0103 WS_Diff_Max_ge_7 1 0.97310.2846 0.4153 1.5309 3.42 0.0006

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut-pointsBP 24 hr_diff Mean ≤ 0.0 Yes vs. No 3.23 1.32 7.93 0.01 WS_24 hr diffMax ≥ 7 Yes vs. No 2.65 1.51 4.62 <0.01

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Mean_Low)+β₂(WS_Diff_Max_ge_7)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_Low)+β) ²^((WS_Diff_Max_ge_7)])+(N)+ε  First Model Equation:

Second Model Equation for lower BP tertile, F/W/S season: (estimated){circumflex over (β)}₀=−6.1660; {circumflex over (β)}₁=1.2907 and{circumflex over (β)}₂=0.8440.

Model Information Data Set WORK.FWS_LOW_BP_2 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (200 levels) Subject Effect Date (90 levels) Number ofClusters 90 Correlation Matrix 200 Dimension Maximum Cluster Size 99Minimum Cluster Size 28

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.1660 0.4181 −6.9854 −5.3466 −14.75 <.0001 BP_Diff_Mean_Low1 1.2907 0.3985 0.5097 2.0717 3.24 0.0012 WS_Diff_Max_ge_7 1 0.84400.2815 0.2923 1.3958 3.00 0.0027

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut-pointsBP_24 hr diff Mean ≤ −0.05 Yes vs. No 3.64 1.66 7.94 <0.01 WS_24 hr diffMax ≥ 7 Yes vs. No 2.33 1.34 4.04 <0.01

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Mean_Low)+β₂(WS_Diff_Max_ge_7)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_Low)+β) ²^((WS_Diff_Max_ge_7)])+(N)+ε  Second Model Equation:

Third Model Equation for lower BP tertile, F/W/S season: (estimated){circumflex over (β)}₀=−5.8445; {circumflex over (β)}₁=1.1687 and{circumflex over (β)}₂=0.7252

Model Information Data Set WORK.FWS_LOW_BP_3 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (200 levels) Subject Effect Date (90 levels) Number ofClusters 90 Correlation Matrix 200 Dimension Maximum Cluster Size 99Minimum Cluster Size 28

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −5.8445 0.3159 −6.4637 −5.2253 −18.50 <.0001 BP_Diff_Mean_Low1 1.1687 0.3047 0.5715 1.7659 3.84 0.0001 WS_Diff_Max_ge_7 1 0.72520.2726 0.1909 1.2594 2.66 0.0078

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut-pointsBP_24 hr diff Mean ≤ −0.10 Yes vs. No 3.22 1.77 5.85 <0.01 WS_24 hr diffMax ≥ 7 Yes vs. No 2.07 1.21 3.52 0.01

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Mean_Low)+β₂(WS_Diff_Max_ge_7)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_Low)+β) ²^((WS_Diff_Max_ge_7)])+(N)+ε  Third Model Equation:

Fourth Model Equation for lower BP tertile, F/W/S season:For the fourth model equation,The intercept is represented by β₀ and is estimated such that{circumflex over (β)}₀−6.5086First predictor variable is BP 24 hr diff Mean,

The coefficient for the first predictor variable is β₁ and is estimatedsuch that {circumflex over (β)}₁=−4.4858.

The second predictor variable is (BP 24 hr diff Mean)²,

The coefficient for the second predictor variable is β₂ and is estimatedsuch that {circumflex over (β)}₂=−2.1769.

The third predictor variable is WS 24 hr diff Max

The coefficient for the third predictor variable is β₃ and is estimatedsuch that {circumflex over (β)}₃=0.2750. The fourth predictor variableis (WS 24 hr diff Max)².

The coefficient for the fourth predictor variable is β₄ and is estimatedsuch that {circumflex over (β)}₄=−0.0111.

The offset term is log(N), where N=the number of patients eligible tohave a NOH on the given day.The error term of the regression model is represented by “ε”.

Model Information Data Set WORK.FWS_LOW_BP_4 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (200 levels) Subject Effect Date (90 levels) Number ofClusters 90 Correlation Matrix 200 Dimension Maximum Cluster Size 99Minimum Cluster Size 28

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.5086 0.6736 −7.8288 −5.1884 −9.66 <.0001 BP_24 HR_DIFF_Mean−4.4858 2.2688 −8.9326 −0.0391 −1.98 0.0480 BP_diff_mean_sq −2.17695.8365 −13.6162 9.2624 −0.37 0.7092 WS_24 HR_DIFF_Maximum 0.2750 0.12980.0206 0.5294 2.12 0.0341 WS_diff_max_sq −0.0111 0.0056 −0.0222 −0.0001−1.97 0.0486

Parameter Variable RR Lower 95% Cl Upper 95% Cl p-value BP 24 hr diffMean  0.1 unit increase 0.64 0.41 1.00 0.05 (BP 24 hr diff Mean)² 0.01unit increase 0.98 0.87 1.10 0.71 WS 24 hr diff Max   5 unit increase3.96 1.11 14.11 0.03 (WS 24 hr diff Max )²   25 unit increase 0.76 0.571.00 0.05

log(UT-IR-NOH Day)=β₀+β₁(BP 24 hr diff Mean)+β₂(BP 24 hr diffMean)²+β₃(WS 24 hr diff Max)+β₄(WS 24 hr diff Max)² log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP 24hr diff Mean)+β) ²^((BP 24hr diff Mean)) ² ^(+β) ³ ^((WS 24hr diff Max)+β) ⁴^((WS 24hr diff Max)) ² ^(+log(N)+ε])+(N)+ε  Fourth Model Equation:

Example 3

This example illustrates generation of model equations for middletertile BP days in the F/W/S season. For the first and second modelequations:

Outcome variable: UT-IR-NOH

1=Yes; the day is a UT-IR-NOH day for the season

0=No; the day is not a UT-IR-NOH day for the season

The intercept is represented by β₀

First predictor variable: BP_Diff_Mean_Low

1=Yes; the day had a BP_24hr_Diff_Mean ≤0.0

0=No; the day did not have a BP_24hr_Diff_Mean ≤0.0

The coefficient for the predictor variable BP_Diff_Mean_Low isrepresented by β₁

Second predictor variable: WS_Diff_Max_ge_6

1=Yes; the day had a WS_24hr_Diff_Max ≥6

0=No; the day did NOT have a WS_24hr_Diff_Max ≥6

The coefficient for the predictor variable WS_Diff_Max_ge_7 isrepresented by β₂

Offset term—variable log(N), where N=the number of patients eligible tohave a NOH on the given day.Error term of GEE regression model represented by “ε”.First Model Equation for middle BP tertile in F/W/S season: {circumflexover (β)}₀=−6.3411; {circumflex over (β)}₁=0.7397 and {circumflex over(β)}₂=0.8112.

Model Information Data Set WORK.FWS_AVG_BP_1 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (205 levels) Subject Effect Date (91 levels) Number ofClusters 91 Correlation Matrix 205 Dimension Maximum Cluster Size 92Minimum Cluster Size 35

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.3411 0.5583 −7.4353 −5.2468 −11.36 <.0001 BP_Diff_Mean_Low1 0.7397 0.4279 −0.0990 1.5784 1.73 0.0839 WS_Diff_Max_ge_6 1 0.81120.4513 −0.0734 1.6957 1.80 0.0723

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut-pointsBP_24 hr diff Mean ≤ 0.0 Yes vs. No 2.10 0.91 4.85 0.08 WS_24 hr diffMax ≥ 6 Yes vs. No 2.25 0.93 5.45 0.07

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Mean_Low)+β₂(WS_Diff_Max_ge_6)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean Low)+β) ²^((WS_Diff_Max_ge_6)])+(N)+ε  First Model Equation:

Second Model Equation for middle BP tertile in F/W/S season: {circumflexover (β)}₀=−6.2028; {circumflex over (β)}₁=1.0064 and {circumflex over(β)}₂=0.5680.

Model Information Data Set WORK.FWS_AVG_BP_2 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (205 levels) Subject Effect Date (91 levels) Number ofClusters 91 Correlation Matrix 205 Dimension Maximum Cluster Size 92Minimum Cluster Size 35

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.2028 0.4588 −7.1021 −5.3035 −13.52 <.0001 BP_Diff_Mean_Low1 1.0064 0.3913 0.2395 1.7733 2.57 0.0101 WS_Diff_Max_ge_6 1 0.56800.4610 −0.3355 1.4716 1.23 0.2179

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- BP 24Hr diff Mean ≤ −0.05 Yes vs. No 2.74 1.27 5.89 0.01 points WS 24 hr_diffMax ≥ 6 Yes vs. No 1.76 0.72 4.36 0.22

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Mean_Low)+β₂(WS_Diff_Max_ge_6)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_Low)+β) ²^((WS_Diff_Max_ge_6)])+(N)+ε  Second Model Equation:

Similarly, a Third and Fourth Model Equation were generated and are setforth below:

24 HR BP diff mean <=−0.05 and RH mean >=79

log(Upper Tertile HeadacheDay)=β₀+β₁(BP_Diff_Mean_Low)+β₂(RH_Daily_Mean_ge_79)+log(N)+ε

Or equivalently,

Upper Tertile Headache Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_Low)+β) ²^((RH_Daily_Mean_ge_79)])+(N)+ε  Third Model Equation:

log(Upper Tertile Headache Day)=β₀+β₁(BP_24h_Diff_Mean_le_0.10)+β₂(RH_Daily_Mean_ge_78)+log(N)+ε

Or equivalently,

Upper Tertile Headache Day=e ^([β) ⁰ ^(+β) ¹^((BP_24h_Diff_Mean_≤0.10)+β) ² ^((RH_Daily_Mean_ge_78)])+(N)+ε  FourthModel Equation:

In other specific embodiments the significant weather variables areBP_24 h_Diff_Mean_le_neg_0.05 and RH_Daily_Mean_ge_79

Example 4

This example illustrates generation of model equations for upper tertileBP days in the F/W/S season,

For the first and second model equations:Outcome variable: UT-IR-NOH

1=Yes; the day is a UT-IR-NOH day for the season

0=No; the day is not a UT-IR-NOH day for the season

The intercept is represented by β₀

First predictor variable: BP_Diff_Mean_High

1=Yes; the day had a BP_24hr_Diff_Mean 0.10

0=No; the day did not have a BP_24hr_Diff_Mean_0.10

The coefficient for the predictor variable BP_Diff_Mean_High isrepresented by β₁

Second predictor variable: DBT_24hr_diff_mean_cutpoint

1=Yes; the day had a DBT_24hr_diff_mean ≤−5

0=No; the day did NOT have a DBT_24hr_diff_mean ≤−5

The coefficient for the predictor variable DBT_24hr_diff_mean_cutpointis represented by β₂

Offset term—variable log(N), where N=the number of patients eligible tohave a NOH on the given day.Error term of GEE regression model represented by “ε”.First Model Equation for upper BP tertile in the F/W/S season:{circumflex over (β)}₀=−6.7779; {circumflex over (β)}₁=1.5806 and{circumflex over (β)}₂=1.2285.

Model Information Data Set WORK.FWS_HIGH_BP_1 Distribution Poisson LinkFunction Log Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (206 levels) Subject Effect Date (92 levels) Number ofClusters 92 Correlation Matrix 206 Dimension Maximum Cluster Size 98Minimum Cluster Size 35

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.7779 0.4418 −7.6439 −5.9120 −15.34 <.0001BP_Diff_Mean_cutpoint 1 1.5806 0.4979 0.6047 2.5565 3.17 0.0015 DBT_24Hr_Mean_cutpoint 1 1.2285 0.3617 0.5196 1.9374 3.40 0.0007

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- BP_24Hr diff Mean ≥ 0.10 Yes vs. No 4.86 1.83 12.89 <0.01 points DBT_24 Hrdiff Mean ≤ −5 Yes vs. No 3.42 1.68 6.94 <0.01

log(UT-IR-NOHDay)=β₀+β₁(BP_Diff_Mean_High)+β₂(DBT_24hr_diff_Mean_cutpoint)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_High)+β) ²^((DBT_24hr_diff_Mean_cutpoint)])+log(N)+ε  First Model Equation:

Second Model Equation for upper BP tertile, F/W/S season, {circumflexover (β)}₀=−6.7684; {circumflex over (β)}₁=1.8818 and {circumflex over(β)}₂=0.6563.For this equation, the second predictor variable changes.Second predictor variable: DBT_6 hr_diff_mean_cutpoint

1=Yes; the day had a DBT_6 hr_diff_mean ≤−5

0=No; the day did NOT have a DBT_6 hr_diff_mean ≤−5

The coefficient for the predictor variable DBT_6 hr_diff_mean_cutpointis represented by β₂

Model Information Data Set WORK.FWS_UPPER_BP_2 Distribution Poisson LinkLog Function Dependent Upper_Tertile_FWS Variable Offset LN_N Variable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (206 levels) Subject Effect Date (92 levels) Number ofClusters 92 Correlation Matrix 206 Dimension Maximum Cluster Size 98Minimum Cluster Size 35

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −6.7684 0.4813 −7.7118 −5.8250 −14.06 <.0001BP_Diff_Mean_cutpoint 1 1.8818 0.4903 0.9208 2.8427 3.84 0.0001 DBT_6Hr_Mean_cutpoint 1 0.6563 0.3428 −0.0155 1.3281 1.91 0.0555

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- BP_24hr diff Mean ≥ 0.10 Yes vs. No 6.57 2.51 17.16 <0.01 points DBT 6 HRdiff Mean ≤ −0.5 Yes vs. No 1.93 0.98 3.77 0.06

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Mean_High)+β₂(DBT_6hr_diff_Mean_cutpoint)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_High)+β) ²^((DBT_6hr_diff_Mean_cutpoint)])+log(N)+ε  Second Model Equation:

Similarly, a third model equation for UT-BP F/SW was generated:

log(Upper Tertile HeadacheDay)=β₀+β₁(BP_Diff_Mean_High)+β₂(RH_Diff_Min_le_neg_25)+log(N)+ε

Or equivalently,

Upper Tertile Headache Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Mean_High)+β) ²^((RH_Diff_Min_le_neg_25)])+(N)+ε

In other specific embodiments the significant weather variables wereBP_Diff_Mean_ge_0.10 and RH_Diff_Min_le_neg_25

Example 5

This example illustrates generation of model equations for lower tertileBP days in the Summer season.

Outcome variable: UT-IR-NOH

1=Yes; the day is a UT-IR-NOH day for the season

0=No; the day is not a UT-IR-NOH day for the season

The intercept is represented by β₀

First predictor variable: BP_Diff_Max_Low

1=Yes; the day had a BP_24hr_Diff_Max ≤−0.01

0=No; the day did not have a BP_24hr_Diff_Max ≤−0.01

The coefficient for the predictor variable BP_Diff_Max_Low isrepresented by β₁

Offset term—variable log(N), where N=the number of patients eligible tohave a NOH on the given day.Error term of GEE regression model represented by “ε”.First Model Equation for lower BP tertile in the Summer season:{circumflex over (β)}₀=−4.9774, {circumflex over (β)}₁=1.3396

Model Information Data Set WORK.SUMMER_LOW_1 Distribution Poisson LinkLog Function Dependent Upper_Tertile_Summer_both Variable Offset LN_NVariable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (111 levels) Subject Effect Date (47 levels) Number ofClusters 47 Correlation Matrix 111 Dimension Maximum Cluster Size 55Minimum Cluster Size 15

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −4.9774 0.4198 −5.8001 −4.1547 −11.86 <.0001 BP_24hr_Max_cutpoint 1 1.3396 0.4594 0.4392 2.2400 2.92 0.0035

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- BP 24hr Max ≤ −0.01 Yes vs. No 3.82 1.55 9.39 <0.01 point

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Max_Low)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Max_Low)])+(N)+ε  First ModelEquation:

Second Model Equation for lower BP tertile, Summer season: {circumflexover (β)}₀=−5.3481, {circumflex over (β)}₁=1.7615

Model Information Data Set WORK.SUMMER_LOW_2 Distribution Poisson LinkLog Function Dependent Upper_Tertile_Summer_both Variable Offset LN_NVariable

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (111 levels) Subject Effect Date (47 levels) Number ofClusters 47 Correlation Matrix 111 Dimension Maximum Cluster Size 55Minimum Cluster Size 15

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −5.3481 0.5194 −6.3661 −4.3302 −10.30 <.0001 BP_24hr_Max_cutpoint 1 1.7615 0.5473 0.6887 2.8343 3.22 0.0013

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- BP 24hr Max ≤ 0.00 Yes vs. No 5.82 1.99 17.02 <0.01 point

log(UT-IR-NOH Day)=β₀+β₁(BP_Diff_Max_Low)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Diff_Max_Low)])+(N)+ε  SecondModel Equation:

Example 6

This example illustrates generation of model equations for middletertile BP days in the Summer season.

Outcome variable: UT-IR-NOH

1=Yes; the day is a UT-IR-NOH day for the season

0=No; the day is not a UT-IR-NOH day for the season

The intercept is represented by β₀

First predictor variable: BP_Daily_Mean_Low

1=Yes; the day had a BP_Daily_Mean ≤29.44

0=No; the day did not have a BP_Daily_Mean ≤29.44

The coefficient for the predictor variable BP_Daily_Mean_Low isrepresented by β₁

Second predictor variable: DBT_Daily_Mean_le_77

1=Yes; the day had a DBT_Daily_Mean ≤77

0=No; the day did not have a DBT_Daily_Mean ≤77

The coefficient for the predictor variable DBT_Daily_Mean_le_77 isrepresented by β₂Offset term—variable log(N), where N=the number of patients eligible tohave a NOH on the given day.Error term of GEE regression model represented by “ε”.First Model Equation for middle BP tertile in the Summer season:{circumflex over (β)}₀=−5.5947, {circumflex over (β)}₁=1.2594, β₂=1.2393

Model Information Data Set WORK.SUMMER_MIDDLE_1 Distribution PoissonLink Log Function Dependent Upper_Tertile_Summer_both Variable OffsetLN_N Variable

GEE Model Information Correlation Independent Structure Within- ID (108levels) Subject Effect Subject Date (48 levels) Effect Number of 48Clusters Correlation 108 Matrix Dimension Maximum 54 Cluster SizeMinimum 15 Cluster Size

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −5.5947 0.4338 −6.4449 −4.7445 −12.90 <.0001BP_Daily_Mean_cutpoi 1 1.2594 0.4261 0.4242 2.0945 2.96 0.0031DBT_Daily_Mean_cutpo 1 1.2393 0.3827 0.4892 1.9893 3.24 0.0012

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- BPDaily Mean ≤ 29.44 Yes vs. No 3.52 1.53 8.12 <0.01 point DBT Daily Mean≤ 77 Yes vs. No 3.45 1.63 7.31 <0.01

log(UT-IR-NOHDay)=β₀+β₁(BP_Daily_Mean_Low)+β₂(DBT_Daily_Mean_le_77)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((BP_Daily_Mean_Low)+β) ²^((DBT_Daily_Mean_le_77)])+(N)+ε  First Model Equation:

Example 7

This example illustrates generation of model equations for upper tertileBP days in the Summer season.

Outcome variable: UT-IR-NOH

1=Yes; the day is a UT-IR-NOH day for the season

0=No; the day is not a UT-IR-NOH day for the season

The intercept is represented by β₀

First predictor variable: RH_Diff_Mean_ge_5

1=Yes; the day had a RH_24hr_Diff_Mean ≥5

0=No; the day did not have a RH_24hr_Diff_Mean ≥5

The coefficient for the predictor variable RH_Diff_Mean_ge_5 isrepresented by β₁

Offset term—variable log(N), where N=the number of patients eligible tohave a NOH on the given day.Error term of GEE regression model represented by “ε”.First Model Equation for upper BP tertile in the Summer season:{circumflex over (β)}₀=−4.5228, {circumflex over (β)}₁=1.1376

Model Information Data Set WORK.SUMMER_UPPER_1 Distribution Poisson LinkFunction Log Dependent Variable Upper_Tertile_Summer_both OffsetVariable LN_N

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (108 levels) Subject Effect Date (48 levels) Number ofClusters 48 Correlation Matrix Dimension 108 Maximum Cluster Size 54Minimum Cluster Size 14

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −4.5228 0.2916 −5.0944 −3.9512 −15.51 <.0001 RH_24Hr_Mean_cutpoin 1 1.1376 0.3266 0.4974 1.7778 3.48 0.0005

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- RH 24hr Mean ≥ 5 Yes vs. No 3.12 1.64 5.92 <0.01 point

log(UT-IR-NOH Day)=β₀+β₁(RH_Diff_Mean_ge_5)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ¹ ^((RH_Diff_Mean_ge_5)])+(N)+ε  FirstModel Equation:

Second Model Equation for upper BP tertile in the Summer season:{circumflex over (β)}₀=−4.5292, β₁=1.1860

Model Information Data Set WORK.SUMMER_HIGH_2 Distribution Poisson LinkFunction Log Dependent Variable Upper_Tertile_Summer_both OffsetVariable LN_N

GEE Model Information Correlation Structure Independent Within-SubjectEffect ID (108 levels) Subject Effect Date (48 levels) Number ofClusters 48 Correlation Matrix Dimension 108 Maximum Cluster Size 54Minimum Cluster Size 14

Analysis Of GEE Parameter Estimates Empirical Standard Error EstimatesStandard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z|Intercept −4.5292 0.2917 −5.1009 −3.9575 −15.53 <.0001 RH_24Hr_Mean_cutpoin 1 1.1860 0.3250 0.5491 1.8229 3.65 0.0003

Model Parameter Variable RR Lower 95% CI Upper 95% CI p-value Cut- RH 24hr Mean ≥ 7 Yes vs. No 3.27 1.73 6.19 <0.01 point

log(UT-IR-NOH Day)=β₀+β₁(RH_Diff_Mean_ge_7)+log(N)+ε

Or equivalently,

UT-IR-NOH Day=e ^([β) ⁰ ^(+β) ₁ ^((RH_Diff_Mean_ge_7)])+(N)+ε  SecondModel Equation:

Example 8

The following Example utilizes a bootstrap analysis to provide initialvalidation of the models developed for low, average and high BP days forthe Fall/Winter/Spring season.

In a bootstrap analysis, the original data is re-sampled to create a newdata set. The new data set has some observations from the original datarepeated multiple times, while some observations in the original dataset may not be selected in the new data set. The process is repeatedhundreds or thousands of times to get a large number of “bootstrap” datasets which are all based on the original data set. A regression analysisis run for each bootstrap data set and results are obtained. The resultsare used to estimate each of the statistics involved in the regressionanalysis. For example, if regression analysis is conducted on 1,000bootstrap samples generated from the Low BP data set, 1,000 differentestimates of the RR value for the BP_24-hour difference variable may beobtained (i.e., one RR estimate from each bootstrap data set). The2.5^(th) and 97.5^(th) percentiles of these 1,000 RR estimates are usedto obtain a bootstrap 95% confidence interval for the RR estimate of theBP 24-hour difference variable.

The original data set included multiple observations for each subject;hence rather than re-sampling from each observation, various subjectswithin each BP tertile were re-sampled. Each time a subject is selectedin the bootstrap process, all of the measurements belonging to thatsubject are selected. In this way, the within-subject andbetween-subject covariance structure of the original data set ismaintained. Because some subjects had missing observations for one ormore variables, the bootstrap (or replicate) data sets also containedsome missing observations. Since some subjects had more observation daysthan others, each of the bootstrap data sets will not have the exactsame number of observations.

It was previously observed that the best variables for the Lower,Middle, and Upper BP tertile days were as follows:

-   -   Lower BP→1) BP 24-hour difference Mean+2) Wind Speed 24-hour        difference Maximum    -   Middle BP→1) BP 24-hour difference Mean+2) Wind Speed 24-hour        difference Maximum    -   Upper BP→1) BP 24-hour difference Mean+2) Dry Bulb Temp. 24-hour        difference Mean

For each BP tertile, a generalized additive model (GAM) using theoriginal data set was performed to determine the potential cut-pointsfor each variable. A GEE regression analysis was performed for the“best” cut-point model using the original data set. The results of theGAM and GEE analyses for Lower, Middle and Upper Barometric Pressure(BP) days are set forth in FIG. 5A-B, FIG. 6A-B and FIG. 7A-B,respectively.

Based on the potential cut-points from the GAM analyses, several GEEanalyses using the bootstrap data sets were performed using differentcombinations of cut-points for the two variables. For each BP tertile,1,000 bootstrap data sets were generated. The GEE regression analysiswas performed for each bootstrap data set. Based on the results of the1,000 data sets, the bootstrap 95% confidence intervals were determinedfor each statistic in the GEE regression.

The following cut-point combinations were assessed in the bootstrapanalysis:

Lower BP Middle BP Upper BP BP ≤ 0.0, WS ≥7 BP ≤ 0.0,WS ≥ 6 BP > 0.1,DBT < −10 BP ≤ 0.0, WS ≥ 11 BP ≤ 0.0, WS ≥ 8 BP > 0.1, DBT < −5 BP ≤0.0, WS ≥ 15 BP ≤ 0.0, WS ≥ 11 BP > 0.1, DBT < 0 BP ≤ 0.1, WS ≥ 7 BP ≤0.1, WS ≥ 6 BP > 0.1, DBT < 5 BP ≤ 0.1, WS ≥ 11 BP ≤ 0.1, WS ≥ 8 BP >0.3, DBT < −10 BP ≤ 0.1, WS ≥ 15 BP ≤ 0.1, WS ≥ 11 BP > 0.3, DBT < −5 BP≤ −0.1, WS ≥ 7 BP ≤ −0.1, WS ≥ 6 BP > 0.3, DBT < 0 BP ≤ −0.1, WS ≥ 11 BP≤ −0.1, WS ≥ 8 BP > 0.3, DBT < 5 BP ≤ −0.1, WS ≥ 15 BP ≤ −0.1, WS ≥ 11BP > 0.4, DBT < −10 BP ≤ −0.2, WS ≥ 7 BP ≤ −0.2, WS ≥ 6 BP > 0.4, DBT <−5 BP ≤ −0.2, WS ≥ 11 BP ≤ −0.2, WS ≥ 8 BP > 0.4, DBT < 0 BP ≤ −0.2, WS≥ 15 BP ≤ −0.2, WS ≥ 11 BP > 0.4, DBT < 5 BP ≤ −0.3, WS ≥ 7 BP ≤ −0.3,WS ≥ 11 BP ≤ −0.3, WS ≥ 15

Results of each combination of cut-points were compared and the “best”bootstrap models were selected. The output for the models selected aresummarized in FIG. 5C for Lower BP tertile days, FIG. 6C for Middle BPtertile days, and FIG. 7C for Upper BP tertile days. For each predictorvariable, the output consists of the mean value and 95% confidenceinterval for the following statistics: the RR estimate, the Lower Cl ofthe RR, the Upper Cl of the RR, the p-value estimate, and the QIC fitstatistic estimate.

For example, in the analysis of the Lower BP tertile days (FIGS. 5A andB) there appeared to be two models that performed better than the rest.The first of these models involved using the cut-points of BP 24-hourdifference mean ≤0.0 and WS_24-hour difference Max ≥7. The bootstrapanalysis results for this model are summarized in Model 1 of FIG. 5C.The mean RR estimate for the BP variable across the 1,000 bootstrap datasets are 3.24. The 95% confidence interval for this RR estimate acrossthe 1,000 bootstrap data sets was (2.83, 3.78). The mean estimate of theLower Cl for the RR of the BP variable was 1.32 with a 95% Cl of (1.20,1.47), across the 1,000 bootstrap data sets. The other results for theother statistics can be interpreted in a similar fashion.

Example 9

The following example utilizes a bootstrap analysis to provide initialvalidation for the optimal models developed for the Lower, Middle andUpper BP days for the Summer season. Previously, we had observed thatthe best variables for the Lower, Middle, and Upper BP tertile days wereas follows:

-   -   Lower BP→1) BP 24-hour difference Max    -   Middle BP→1) BP Daily Mean+2) DBT Daily Mean    -   Upper BP→1) RH 24-hour Difference Mean        For each BP tertile, a generalized additive model (GAM) using        the original data set was performed to observe the potential        cut-points for each variable (FIGS. 8A, 9A and 10A), for lower,        middle and upper BP tertile respectively. Then, a GEE regression        analysis was performed for our “best” cut-point model using the        original data set (FIGS. 8B, 9B and 10B).

Based on the potential cut-points from the GAM analyses, several GEEanalyses using the bootstrap data sets were performed using differentcombinations of cut-points for the two variables. For each BP tertile,1,000 bootstrap data sets were generated. The GEE regression analysiswas performed for each bootstrap data set. Based on the results of the1,000 data sets, the bootstrap 95% confidence intervals were determinedfor each statistic in the GEE regression.

The following cut-point combinations were assessed in the bootstrapanalysis:

Lower BP Middle BP Upper BP BP ≤ 0.01 BP ≤ 29.42, DBT ≤ 71 RH ≥ −2 BP ≤0.00 BP ≤ 29.42, DBT ≤ 74 RH ≥ 0 BP ≤ 0.05 BP ≤ 29.42, DBT ≤ 77 RH ≥ 5BP ≤ 0.09 BP ≤ 29.44, DBT ≤ 71 RH ≥ 7 BP ≤ 0.10 BP ≤ 29.44, DBT ≤ 74 BP≤ 29.44, DBT ≤ 77 BP ≤ 29.475, DBT ≤ 71 BP ≤ 29.475, DBT ≤ 74 BP ≤29.475, DBT ≤ 77

Results for each combination of cut-points were compared and the “best”bootstrap models were selected. The output for the best models aresummarized in FIGS. 8C, 9C and 10C for lower, middle and upper BPtertile days, respectively. For each predictor variable, the outputconsists of the mean value and 95% confidence interval for the followingstatistics: the RR estimate, the Lower Cl of the RR, the Upper Cl of theRR, the p-value estimate, and the QIC fit statistic estimate.

For example, in the analysis of the Lower BP days there were two modelsselected as “best.” Model 1 (FIG. 8C) involved using the cut-points ofBP 24-hour difference Max ≥−0.01. The mean RR estimate for the BPvariable across the 1,000 bootstrap data sets was 3.82. The 95%confidence interval for this RR estimate across the 1,000 bootstrap datasets was (3.19, 4.62). The mean estimate of the Lower Cl for the RR ofthe BP variable was 1.54 with a 95% Cl of (1.32, 1.77), across the 1,000bootstrap data sets. The other results for the other statistics can beinterpreted in a similar fashion.

Example 9

This example illustrates how an individual patient who suffers fromweather-associated migraine headaches can utilize a predictive modelaccording to the some embodiments of the invention to manage mitigatingand preventative treatment. Patient A suffers from migraines. Patient Ais planning an important schedule item on Aug. 2, 2015. Patient A wantsto know the likelihood that she will suffer a migraine headache on Aug.2, 2015. Patient A lives in Lexington, Ky., which is climate region Cfa,and the season is Summer. Predicted hourly weather data, including BP,RH, DBT WD and WS are gathered for August 1 and August 2. The predictedBP for August 2 is determined and August 2 is classified as an upper,middle or lower BP tertile day. The appropriate equation is selectedbased on BP tertile, season and climate region; weather variable datafor the appropriate model equation are entered, and the risk isdetermined. If the risk is greater than 50%, Patient A begins takingpreventative medication on August 1.

In some embodiments, the model equations may be generated frompopulation data and weather data for the climate region across a timeframe that includes all relevant seasons of the climate region. In moreindividualized regimens, model equations may generated from individualdata and weather data for a climate region across a time frame thatincludes all relevant seasons of the climate region. In some embodimentsthe equations are dynamic and evolve in accordance with entered data ona continuous basis. In specific embodiments a program implementing apopulation data-generated model equation may be adaptable in response touser input of individual data such that the model automatically updatesand conforms to the most recent entered data.

Predictive model equations according to embodiments of the invention maybe generated similarly for any disease or medical condition which isweather-associated with respect to manifestation of symptoms. Populationmodels, which are generally applicable to an individual in themodel-specific climate region, may be generated by gatheringsymptom/flare-up/onset data for a patient cohort across a time framethat includes the seasons relevant to the climate region (for example,it is contemplated that data collected in the Köppen-Geiger climateclassifications A and E may be subject to one relevant season, whiledata collected in classifications B, C and D may be subject to multiplerelevant seasons depending on the medical condition/disease sensitivityto a season affect). Hourly weather data is gathered across the sametime frame. Data includes, for example, the max, min, mean of barometricpressure, relative humidity, dew point temperature, dry bulbtemperature, wind direction, wind speed, precipitation, anddifferentials of all weather parameters. The days are identified for arelevant season and the days within each season are placed intoquantiles (in specific embodiments, tertiles) based on mean daily BP sothat there is at least an upper, lower and middle quantile. Models aregenerated according to embodiments of the invention and the season andBP quantile are used to determine the appropriate model. To predict riskon a future day, the season and predicted BP quantile are used to selectthe appropriate model for a given climate region, and weather datagathered for the future day and the day immediately prior to the futureday (in order to determine differentials) are entered into the equationsand a risk is assessed. The patient may then initiate mitigating orpreventative treatment to reduce the risk, or utilize the riskassessment to schedule around high-risk days.

It is expressly contemplated that each of the various aspects,embodiments, and features thereof described herein may be freelycombined with any or all other aspects, embodiments, and features. Theresulting aspects and embodiments (e.g., models and methods) are withinthe scope of the invention. It should be understood that headings hereinare provided for purposes of convenience and do not imply any limitationon content included below such heading or the use of such content incombination with content included below other headings.

All articles, books, patent applications, patents, other publicationsmentioned in this application are incorporated herein by reference. Inthe event of a conflict between the specification and any of theincorporated references the specification (including any amendmentsthereto) shall control. Unless otherwise indicated, art-acceptedmeanings of terms and abbreviations are used herein.

In the claims articles such as “a”, “an” and “the” may mean one or morethan one unless indicated to the contrary or otherwise evident from thecontext. Claims or descriptions that include “or” between one or moremembers of a group are considered satisfied if one, more than one, orall of the group members are present in, employed in, or otherwiserelevant to a given product or process unless indicated to the contraryor otherwise evident from the context. The invention includesembodiments in which exactly one member of the group is present in,employed in, or otherwise relevant to a given product or process. It isto be understood that the invention encompasses all variations,combinations, and permutations in which one or more limitations,elements, clauses, descriptive terms, etc., from one or more of thelisted claims is introduced into another claim. For example, any claimthat is dependent on another claim may be modified to include one ormore elements, limitations, clauses, or descriptive terms, found in anyother claim that is dependent on the same base claim. Furthermore, wherethe claims recite a product, it is to be understood that methods ofusing the product according to any of the methods disclosed herein, andmethods of making the product, are included within the scope of theinvention, unless otherwise indicated or unless it would be evident toone of ordinary skill in the art that a contradiction or inconsistencywould arise.

Where elements are presented as lists, it is to be understood that eachsubgroup of the elements is also disclosed, and any element(s) may beremoved from the group. The invention provides all such embodiments.

The terms “approximately” or “about” in reference to a number generallyinclude numbers that fall within ±10%, in some embodiments ±5%, in someembodiments ±1%, in some embodiments ±0.5% of the number unlessotherwise stated or otherwise evident from the context (except wheresuch number would impermissibly exceed 100% of a possible value). Whereranges are given, endpoints are included. Furthermore, it is to beunderstood that unless otherwise indicated or otherwise evident from thecontext and understanding of one of ordinary skill in the art, valuesthat are expressed as ranges may assume any specific value or subrangewithin the stated ranges in different embodiments of the invention, tothe tenth of the unit of the lower limit of the range, unless thecontext clearly dictates otherwise. Any one or more embodiment(s),element(s), feature(s), aspect(s), component(s) etc., of the presentinvention may be explicitly excluded from any one or more of the claims.

Those skilled in the art will recognize, or be able to ascertain usingno more than routine experimentation, many equivalents to the specificembodiments of the invention described and exemplified herein. The scopeof the present invention is not intended to be limited to the aboveDescription and Examples, but rather is as set forth in the appendedclaims.

1. A method for generating a model set of equations for predicting arisk of a subject who experiences adverse medical events associated withthe weather, of experiencing a new-onset event (NOE), the methodcomprising: a) identifying a climate region of interest; b) collectingdaily mean barometric pressure (BP) data for a time frame and dividingthe days of the time frame into at least upper, middle and lowerquantile BP days to identify the upper quantile BP days; c) collectingdaily NOE data for a subject cohort consisting of subjects known tosuffer from the adverse medical event for the time frame and calculatinga daily incident rate (IR) of NOEs for each day of the time frame anddividing the days of the time frame into at least upper, middle andlower quantile IR-NOE days to identify the upper quantile IR-NOE(UQ-IR-NOE) days; d) determining a relevant number of seasons based onan association between the upper IR-NOE quantile days identified in c)and the upper BP quantile days identified in b); e) collecting hourlyweather data for the time frame for a number of weather parameters anddetermining a set of weather variables; f) employing a generalizedlinear regression analysis to generate a rank for each weather variableas a predictor of the UQ-IR-NOE days for each relevant season, for eachBP quantile; g) identifying a predictive equation using a forwardstepwise approach, wherein the model comprises a set of one or moreequations for predicting the risk of a subject experiencing a new-onsetevent (NOE) at the completion of step (g).
 2. The method according toclaim 1, wherein the number of relevant seasons is 2-4 and the timeframe is one year.
 3. The method of claim 1, wherein the generalizedlinear regression analysis of step (f) comprises a generalized mixedanalysis or a generalized estimating equation (GEE) analysis;
 4. Themethod of claim 3, wherein the predictor of step (f) is continuous. 5.The method of claim 4, wherein the generalized linear regressionanalysis of step (f) comprises GEE and the forward stepwise approach ofstep (g) comprises the following steps: i) identifying a best predictivesingle variable equation based on p-value and quasi-likelihoodindependence criterion (QIC) fit of the first-ranked weather variable ineach season, for each BP quantile; ii) adding the next-ranked weathervariable to the identified equation from g) in each season, for each BPand determine if fit improves; iii) repeating step (ii) until additionof the next-ranked weather variable to the model fails to improve fit.6. The method according to claim 4, wherein the generalized linearregression analysis of step (f) comprises a generalized mixed regressionanalysis and the forward stepwise approach of step (g) comprises thefollowing steps: i) identifying a best predictive single variableequation based on Akaike information criterion (AIC) fit of thefirst-ranked variable in each season, for each BP quantile; ii) addingthe next-ranked weather variable to the identified equation from (g) ineach season, for each BP and determine if fit improves; iii) repeatingstep (ii) until addition of the next-ranked variable to the model failsto improve fit.
 7. The method according to 1, wherein the number ofseasons determined in step (d) is based on a regression analysis of theUQ-BP and the UQ-IR-NOE, said regression analysis comprising one or bothof leverage point and outlier detection diagnostics.
 8. The methodaccording to claim 7, wherein a daily incident rate is equal to thenumber of subjects experiencing a NOE divided by the total number ofeligible subjects; “eligible subject” being defined as a subject who hasnot experienced an event in the preceding 24 hours.
 9. The methodaccording to claim 1, wherein the weather variables are based on weatherparameters selected from the group consisting of barometric pressure(BP), wind speed (WS), wind direction (WD), dry bulb temperature (DBT),lightening activity (LA), precipitation (P) and relative humidity (RH).10. The method according to claim 9, wherein the weather variablescomprise a daily mean and multiple differential maximums, minimums andmeans for each selected parameter.
 11. The method according to claim 10,wherein the multiple differentials are selected from a 24 hourdifferential, a 12 hour differential, a 6 hour differential a 3 hourdifferential, and combinations thereof for each selected parameter. 12.The method according to claim 8, wherein collected data is collectedfrom multiple geographic locations within the climate region.
 13. Themethod according to claim 12, wherein the climate region is classifiedas Cfa in the Köppen-Geiger climate region classification system and therelevant seasons comprise F/W/S (9/21-6/20) and Summer (6/21-9/20). 14.The method according to claim 13, wherein the weather associated adverseevent is new onset of a migraine headache (NOE=NOH), the quantile is atertile and the model set of equations includes the following weathervariables: A) BP 24 hour differential mean; B) WS_24 hour differentialmaximum; C) DBT_24 hour differential mean; D) DBT_6 hour differentialmean; E) BP 24 hour differential maximum; F) DBT daily mean; G) BP dailymean; and H) RH_24 hour differential mean.
 15. A model set of equationsgenerated according to the method of claim
 12. 16. A model set ofequations generated according to the method of claim 14, wherein R=riskof a given day being a UT-IR-NOH day, the model set of equationscomprising:
 1. [season=F/W/S, BP tertile=lower]R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(B]) +N+ε or 1=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ²^(A(exp)2+β) ³ ^(B+β) ⁴ ^(B(exp)2]) +N+ε
 2. [season=F/W/S, BPtertile=middle]R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(B]) +N+ε
 3. [season=F/W/S, BPtertile=upper]R=e ^([β) ⁰ ^(+β) ¹ ^(A+β) ² ^(C]) +N+ε
 4. [season=Summer, BPtertile=lower]R=e ^([β) ⁰ ^(+β) ¹ ^(E]) +N+ε
 5. [season=Summer, BP tertile=middle]R=e ^([β) ⁰ ^(+β) ¹ ^(G+β) ² ^(F]) +N+ε
 6. [season=Summer, BPtertile=upper]R=e ^([β) ⁰ ^(+β) ¹ ^(H]) +N+ε wherein N is the number of subjects inthe cohort eligible to have an NOH on a given day and is the denominatorin the IR-NOH calculation, and c is an error term of GEE regressionmodeling.
 17. A method of assessing a risk of a subject predisposed toexperiencing weather-associated adverse events for experiencing a newonset event on a given day, the method comprising: a) determining aclimate region associated with the geographical location of the subject;b) determining the a relevant season in which the given day falls; c)determining the a projected mean BP for the day and identifying it as anupper, middle or lower quantile BP day; d) selecting an equation fromthe model set of equations according to claim 15 specific to thedetermined climate region, the determined relevant season and thedetermined BP quantile; and e) entering weather variable data for thegiven day into the selected equation to yield an assessment of the risk.18. The method according to claim 17, wherein the weather-associatedadverse event is associated with a condition selected from asthma,emphysema, depression, cardiovascular disease, arthritis,atherosclerosis, and diabetes.
 19. The method according to claim 18,wherein the weather-associated adverse event is associated withatherosclerosis and comprises heart attack or stroke. 20-23. (canceled)24. A method for increasing efficiency in a hospital staffing andresource commitment by predicting high admission days, a “high”admission day being defined as a day falling in an upper quantile of thehospital's daily admissions for a year, the method comprising: 1)generating a model set of equations for predicting a risk of subjectswho suffer from weather-associated medical conditions of being admittedto the hospital, wherein “generating” comprises the steps of: a)identifying the climate region in which the hospital is located; b)collecting daily mean barometric pressure (BP) data for the year anddividing the mean BP data into upper, lower and middle quantiles; c)collecting daily hospital admissions data for a subject cohort for theyear, said subject cohort consisting of subjects known to suffer from aweather-associated medical condition and who have been admitted to ahospital at least once previously due to experiencing an adverse eventassociated with the condition, to calculate a daily admission rate (AR)for each day of the year and to determine an upper quantile of daysassociated with the AR; d) determining a number of relevant seasonsbased on regression analysis of the upper BP quantile days and the upperAR quantile days; e) collecting weather parameter data across the year;f) employing GEE modeling to generate a rank for each weather variableas a continuous predictor of the upper quantile AR days for eachrelevant season, for each BP quantile; g) identifying a best predictivesingle variable equation based on p-value and QIC fit of thefirst-ranked weather variable in each relevant season, for each BPquantile; h) adding the next-ranked weather variable to the identifiedequation from g) in each season, for each BP and determining if fitimproves; i) repeating step h) until addition of the next-ranked weathervariable fails to improve fit, wherein the model comprises a set ofequations for predicting a risk of subjects who suffer fromweather-associated medical conditions of being admitted to the hospitalat the completion of step i); 2) employing the model to determine whichdays are likely to be upper quantile admission rate (UQ-AR) days; and 3)staffing the hospital and committing resources to the hospital on thebasis of the determination in step 2).
 25. An article of manufacturecomprising computer-readable code for implementing the method accordingto claim
 16. 26. The article of manufacture according to claim 25comprising a mobile application software product.